On the role of boundary conditions for CIP stabilization of higher order finite elements.
A posteriori error estimates with post-processing for nonconforming finite elements
For a nonconforming finite element approximation of an elliptic model problem, we propose a posteriori error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited...
Uniformly stable mixed -finite elements on multilevel adaptive grids with hanging nodes
We consider a family of quadrilateral or hexahedral mixed -finite elements for an incompressible flow problem with -elements for the velocity and discontinuous -elements for the pressure where the order can vary from element to element between and an arbitrary bound. For multilevel adaptive grids with hanging nodes and a sufficiently small mesh size, we prove the inf-sup condition uniformly with respect to the mesh size and the polynomial degree.
Error Estimates with Post-Processing for Nonconforming Finite Elements
For a nonconforming finite element approximation of an elliptic model problem, we propose error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is exploited that...
A parameter-free smoothness indicator for high-resolution finite element schemes
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...
On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes
We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with -elements for the velocity and discontinuous -elements for the pressure where the order can vary from element to element between and a fixed bound . We prove the inf-sup condition uniformly with respect to the meshwidth on general quadrilateral and hexahedral meshes with hanging nodes.
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